The grades on a geometry midterm at Almond are normally distributed with $\mu = 85$ and $\sigma = 4.0$. Gabriela earned a $78$ on the exam. Find the z-score for Gabriela's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Gabriela's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{78 - {85}}{{4.0}}} $ ${ z \approx -1.75}$ The z-score is $-1.75$. In other words, Gabriela's score was $1.75$ standard deviations below the mean.